*Stairs to Heaven...!*

**June-17, 2011.**

It was the birthday of Miss

**Sinda**&

**Dinsa**, my dear friends at the office...

Apart frem being identical twins their names are anagrams of each other, & their b'day is a Prime (17) , with their star-sign's constellation being

**Gemini**which also stands fer

**twins**..!! This really made me ponder & smile a bit..

**June-15, 2011.**

Another good friend of mine

**Amod Pandey**, had posted a pic of him completing a marathon in the city of Bangalore. But due to heavy work at the office, I hadn't noticed it at till, late in the night of

**June-17, 2011(Friday)**, while was doing some official work at home, I just see it...& smile...!

...but was feeling a bit feverish & dizzy.

The number on his shirt, caught my attention---

**3649.**

Well, suffice it to say that it drove my impending sleep away, as I began to find patterns in it, & ask my-self a barrage of questions like what is the smallest number with such a pattern, etc...!

**June 18, 2011.**

Sunday. Got reminded by mom that it was Fathers' day !

By now, I had devised a series of numbers with such a pattern...as I saw last night.

I secretly wanted to gift my Pappa something he'll feel happy about--because, he's always stressed the importance of Math ever since I was a child.

And the previous night, I had also submitted my series of numbers to an extensive online search program which would apply all kinds of heuristics & algorithms to check & ensure if this series that I had stumbled upon, was indeed a NEW one, or else the proverbial, old-wine in a new bottle...! Luckily, I received confirmation that the series was indeed NEW..!

Along with this confirmation came the need for lots of formalities---I was asked to fill detailed forms about myself, & provide description about the series, & even give a program to compute the first

*terms of the series...[Else, anyone could reel off some random numbers & name the resulting series fer him/her-self... :)) ]*

**'n'**Anyways, I did that, & was asked to make some subtle changes in my documentation, which I did too.

The series I had submitted was now in the '

**proposed**' state---awaiting detailed analysis by REAL mathematicians & scientists behind the

*, who would take the final decision...*

**Online Encyclopedia of Integer Sequences**Anyway, I immediately fergot all about it---and with absolutely no expectations about it, went to sleep....

The next morning, at office, I was very pleased to find a mail stating that my series had indeed been APPROVED & ALLOCATED...!!!

My lit'l Discovery had changed its status frem

**PROPOSED to APPROVED...!!**

Mine is the 1,91,867'th series 'registered'---though it is actually a kind of generating function for an infinite(?) number of new similar series...! [I only considered

*fer now, since the square has always had mysterious applications w.r.t. the Universe around us...!]*

**n=2****That said, there are TONS of questions to be explored like the following :**

**a)**The beautiful stair-case-like graph(s) of the members of this series...

Click on the below graph if you want to see a sample..! :)

**{**

**Notice the unusual structures on the graph ??**Well, i purposely strove hard to make it look like the

*(with those peculiar*

**stamen****anthers**!)of a

*flower ! :-) How ?? By using the Greek small letter*

**Hibiscus***as the plot 'marker'...! ;))*

**'theta'****}**

**b)**Is the series INFINITE...???? Fer ANY value of

**??**

*n*[My

**conjecture**is that it IS...at-least fer

**]**

*n=2***c)**Any 'weird' places where this series 'pops-up'...??

Well, those r interesting points to ponder about....

And the below lines express my feelings very aptly..

**Love & Best Wishes,**

'eh'! even your name could have been an anagram!

ReplyDeleteCongratulations on your invention!!! You have now become immortal. I wish you do a lot more.

If possible and when it is the right time tell us about the series. Also please try to figure out an application of your series, if not yet.

Good luck!

WOnderful Raghu.. :) Congratulations.. Way to go

ReplyDeleteCongratulations Raghu! I am delighted that you have discovered a new series. You are a star !

ReplyDeleteAll the best